Mean value for the matching and dominating polynomial
Jorge Luis Arocha ; Bernardo Llano
Discussiones Mathematicae Graph Theory, Tome 20 (2000), p. 57-69 / Harvested from The Polish Digital Mathematics Library

The mean value of the matching polynomial is computed in the family of all labeled graphs with n vertices. We introduce the dominating polynomial of a graph whose coefficients enumerate the dominating sets for a graph and study some properties of the polynomial. The mean value of this polynomial is determined in a certain special family of bipartite digraphs.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:270566
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1106,
     author = {Jorge Luis Arocha and Bernardo Llano},
     title = {Mean value for the matching and dominating polynomial},
     journal = {Discussiones Mathematicae Graph Theory},
     volume = {20},
     year = {2000},
     pages = {57-69},
     zbl = {0958.05098},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1106}
}
Jorge Luis Arocha; Bernardo Llano. Mean value for the matching and dominating polynomial. Discussiones Mathematicae Graph Theory, Tome 20 (2000) pp. 57-69. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1106/

[000] [1] J.L. Arocha, Anticadenas en conjuntos ordenados, An. Inst. Mat. Univ. Nac. Autónoma México 27 (1987) 1-21.

[001] [2] C. Berge, Graphs and Hypergraphs (North-Holland, London, 1973).

[002] [3] E.J. Farrell, An introduction to matching polynomials, J. Combin. Theory (B) 27 (1979) 75-86, doi: 10.1016/0095-8956(79)90070-4. | Zbl 0335.05131

[003] [4] M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-completeness (Freeman, New York, 1979). | Zbl 0411.68039

[004] [5] C.D. Godsil and I. Gutman, On the theory of the matching polynomial, J. Graph Theory 5 (1981) 137-144, doi: 10.1002/jgt.3190050203.

[005] [6] C.D. Godsil, Algebraic Combinatorics (Chapman and Hall, New York, 1993).

[006] [7] O.J. Heilmann and E.H. Lieb, Monomers and dimers, Phys. Rev. Lett. 24 (1970) 1412-1414, doi: 10.1103/PhysRevLett.24.1412.

[007] [8] O.J. Heilmann and E.H. Lieb, Theory of monomer-dimer systems, Comm. Math. Phys. 25 (1972) 190-232, doi: 10.1007/BF01877590. | Zbl 0228.05131

[008] [9] M.A. Henning, O.R. Oellermann and H.C. Swart, The diversity of domination, Discrete Math. 161 (1996) 161-173, doi: 10.1016/0012-365X(95)00074-7. | Zbl 0870.05034

[009] [10] N.N. Lebedev, Special Functions and their Applications (Dover, New York, 1972).

[010] [11] L. Lovász, Combinatorial Problems and Exercises (North-Holland, Amsterdam, 1979).

[011] [12] O. Ore, Theory of Graphs (Amer. Math. Soc., Providence, 1962). | Zbl 0105.35401